World Map



World Map with Confirmed and Death Cases

Total Confirmed for each Country

Total Deaths for each Country

Bar Chart



Bar Charts with descending order

Row

Bar Chart Confirmed

Bar Chart Table Deaths

Row

Data Table for Confirmed and Deaths - Cumulated and Daily Cases

Cumulated and Daily Trend



Cumulated and Daily Cases over Time

Row

World

World

Row

Selected Countries

China

Austria

France

Germany

Italy

India

South Korea

Spain

United States of America

Germany - Confirmed

Germany - Deaths

Exponential Growth



Column

Estimation speed of spread of the Coronavirus with Linear Regression

Exponential Growth and Doubling Time \(T\)

Exponential growth over time can be fitted by linear regression if the logarithms of the case numbers is taken. Generally, exponential growth corresponds to linearly growth over time for the log (to any base) data.

The semi-logorithmic plot with base-10 log scale for the Y axis shows functions following an exponential law \(y(t) = y_0 * a^{t/\tau}\) as straight lines. The time constant \(\tau\) describes the time required for y to increase by one factor of \(a\).

If e.g. the confirmed or death cases are growing in \(t-days\) by a factor of \(10\) the doubling time \(T \widehat{=} \tau\) can be calculated with \(a \widehat{=} 2\) by

\(T[days] = \frac {t[days] * log_{10}(2)} {log_{10}(y(t))-log_{10}(y_0)}\)

with

\(log_{10}(y(t))-log_{10}(y_0) = = log_{10}(y(t))/y_0) = log_{10}(10*y_0/y_0) = 1\)

and doubling time

\(T[days] = t[days] * log_{10}(2) \approx t[days] * 0.30\).

For Spain, Italy, Germany we have had a doubling time up to \(T \approx 9-12 days * 0.3 \approx 2.7 - 4 days !!\).

The doubling time \(T\) and the Forecast is calculated for following selected countries: Austria, France, Germany, Italy, India, South Korea, Spain, United States of America

Germany - Trend with Forecast on a linear scale

Forecast Plot - next 14 days

The plot shows the extreme forecast increase in case of unchecked exponentiell growth. The dark shaded regions show 80% rsp. 95% prediction intervals. These prediction intervals are displaying the uncertainty in forecasts based on the linear regression over the past 9 days.

Column

Comparison Exponential Growth

Germany - Example plot with ~linear slope on a log10 scale

Exponential Growth since Jan



Column

Exponential Growth Evaluation

China and South Korea significantly slowed down exponential growth. Therefore, their lines in the chart with the log10 scale no longer have a significant.

Most other countries are still in a phase of more or less unchecked exponentiell growth. For Italy, the reduced exponential growth is reflected in a reduced slope of the cumulated cases.

Column

Exponential Growth since mid of January

Doubling Time / Forecast



Column

Doubling Time and Forecast

The forecasted cases for the next 14 days are calculated ‘only’ from the linear regression of the logarithmic data and are not considering any effects of measures in place. In addition data inaccuracies are not taken into account, especially relevant for the confirmed cases.

Therefore the 14 days forecast is only an indication for the direction of an unchecked exponentiell growth.

Forecast (FC) with linear regression: Doubling Time (days), Forecasted cases tomorrow and Forecasted cases in 14 days
Country Case_Type T_doubling last_day FC_next_day FC_14days
Austria Confirmed 5.8 9’618 11’612 55’112
France Confirmed 5.5 45’170 53’625 273’138
Germany Confirmed 5.4 66’885 80’953 425’886
India Confirmed 5.0 1’251 1’449 8’714
Italy Confirmed 10.0 101’739 112’347 277’518
South Korea Confirmed 67.2 9’661 9’752 11’151
Spain Confirmed 4.9 87’956 109’141 679’654
United States of America Confirmed 3.5 161’807 213’231 2’805’996
World Confirmed 6.4 782’365 895’114 3’624’417
Austria Deaths 2.9 108 142 3’142
France Deaths 3.7 3’030 3’960 44’983
Germany Deaths 2.8 645 874 20’847
India Deaths 3.7 32 41 478
Italy Deaths 7.3 11’591 13’102 44’907
South Korea Deaths 14.8 158 166 306
Spain Deaths 3.8 7’716 10’120 109’211
United States of America Deaths 2.8 2’978 4’099 104’672
World Deaths 5.8 37’582 43’241 204’706

Column

Check of Forecast Accuracy

The forecast accuracy is checked by using the forecast method for the nine days before the past three days (training data). Subsequent forecasting of the past three days enables comparison with the real data of these days (test data).

The comparison is also an early indicator if the exponential growth is declining. However, possible changes in underreporting (in particular the proportion confirmed / actually infected) requires careful interpretation.

Germany - Forecast Accuracy for past three days

Forecast



Column

Forecasting with lagged Predictors

The number of confirmed cases can be used as a time delayed predictor of the number of deaths. This will allow comclusions on the time period confirmed to death. More inportant the country specific case fatality rate (CFR, proportion of deaths from confirmed cases) indicates the country specific testing.

Overall a rough conclusion on the country specific proportion of infected to confirmed cases is feasible if the infection fatality rate (IFR, confiremd cases plus all asymptomatic and undiagnosed infections) is assumed to be country independent and the IFR is known (assumption by RKI ~ 0.56%, bottom of existing estimates, see https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Modellierung_Deutschland.pdf?__blob=publicationFile ).

In the model paper RKI assumes for the

  • Incubation period ~ 5-6 days - Day of infection day until symptoms are upcoming)
  • Hospitalisation +4 days - Admission to the hospital (if needed) after Incubation Period)
  • Average period to death + 11 - if the patient dies, it takes an average of 11 days after admission to the hospital

Depending on the country-specific test frequency (late or early tests), the

*lag_days - time from receipt of the confirmed test result to death, Confirmed to Death, is about 11-13 days.

Note: these methods are also used for example for advertising campaigns. The campaign impact on sales will be some time beyond the end of the campaign, and sales in one month will depend on the advertising expenditure in each of the past few months (see https://otexts.com/fpp3/lagged-predictors.html).

Column

Forecasting Cumulated Deaths with lagged Confirmed Cases

Column

Germany - Example plots for method lagged predictors for Daily Deaths depending on lagged Confirmed Cases

References



Data Source

Data Source

Data files are provided by Johns Hopkins University on GitHub
https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series

  • Data files:
    time_series_covid19_confirmed_global.csv,
    time_series_covid19_deaths_global time_series_covid19_recovered_global.csv

Note: as of 2020-03-27 recovered cases are provided again

The data are visualized on their excellent Dashboard
Johns Hopkins University Dashboard
https://coronavirus.jhu.edu/map.html